Thermodynamic stability of metal complexes

The thermodynamic stability of a metal complex may be represented by a stepwise formation constant (or stability constant) K or an overall stability constant P . The formation of a complex between a metal ion, M, and a ligand, L, is usually a substitution reaction. For example, metal ions in aqueous solution will be present as aqua ions. The reaction for the formation of the first complex could be written as  

The expression can be simplified by removing constants. The number of water molecules attached to each metal ion is constant, and in dilute solutions the concentration of water is essentially constant. The expression becomes 

The stepwise coordination of a ligand L to a metal M to form a complex ML , can 

Overall Stability Constants for Some Complexes with Mono- and Bidentate Ligands in Aqueous Solution at 298 K 

The value of an overall stability constant is the product of the stepwise stability constants Kj to K  

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Tantalum enolate chemistry shows the dichotomy for the carbonylation reaction " of Cp Ta(CH2R)Cl3 with CO which results in the mono-THF adduct of rj -acyl complex Cp Ta(0=CCH2R)Cl3(THF) for R = t-Bu (the acyl group is anionic) but the isomeric enolate Cp Ta((Z)-7j -OCH=CHR)Cl3 for R = p-Tol. This invites the question of the relative thermodynamic stabilities of metal complexes of RCH2CO and RCHCHO and additionally the question of Z vs. E enolate stabilities. Only for organometalhc compounds (X = [M]) do we find examples where RCH2COX is less stable than RCH=CHOX. 

The thermodynamic stability of a complex ML formed from an acceptor metal ion M and ligand groups L may be approached in two different but related ways. (The difference between the two approaches lies in the way in which the formation reaction is presented.) Consistent with preceding sections, an equilibrium constant may be written for the formation reaction. This is the formation constant Kv In a simple approach, the effects of the solvent and ionic charges may be ignored. A stepwise representation of the reaction enables a series of stepwise formation constants to be written (Table 3.5). 

Another important consideration is the thermodynamic stability of the complex. Consider the simplified representation of the interaction between a metal or metal-... 

Amaud-Neu, F. Delgado, R. Chaves, S. Critical evaluation of stability constants and thermodynamic functions of metal complexes of crown ethers (IUPAC Technical Report). PureAppl. Chem. 2003, 75 (1), 71-102. 

In addition to the thermodynamic stability of metal - nncleic acid complexes, the rates at which nucleic acid ligands dissociate from a metal-ion coordination sphere are as important as the thermodynamic stability of the metal-nncleic acid bond. 

A general picture for the mechanism is shown in Scheme 4, which is based upon a theoretical analysis by Thom and Hoffmann. Here distinction between (2) and (2a) reflects the general assumption, supported by calculations, that the insertion step requires the M—H and C==C groups to be cis and coplanar, which need not be the case for the first-formed and/or thermodynamically most stable alkene complex (2). Thom and Hoffmann conclude that most or all metal hydrides will have some pathway that leads to hydrometallation without a large kinetic barrier, so long as none of the key intermediates along the way is too stable. The same inference was drawn for the bent metallocene systems discussed earlier (Figure 1) a kinetic barrier to insertion, found only for the cP-cases, is a consequence of the thermodynamic stabilization of alkene complex (2). ... 

A kinetic study of the hydrolysis of JV-salicylideneaniline (113) in the presence and absence of cobalt(II), nickel(II), copper(II) and zinc(II), using 10% ethanol-water as solvent, has been carried out by Dash and Nanda. The (1 1) Schiff base-metal complexes (ML ) were found to undergo acid-catalyzed hydrolysis at rates decreasing with the thermodynamic stabilities of the complexes, the most thermodynamically stable complexes undergoing the slowest rate of hydrolysis. More recent measurements using high copper(II) to ligand ratios have indicated that the copper(II)-imine is quite stable to hydrolysis at pH 5. 

The thermodynamic stability of a complex can be expressed in terms of a stability constant, which reports the ratio of complexed ligand to free metal and ligand in an equilibrium situation. 

Whilst the synthesis of new transition metal-olefin and -acetylene complexes continues unabated, only a relatively small amount of data has accumulated on the thermodynamic stability of these complexes and these are restricted almost exclusively to complexes of the unsatured species acting as monodentate ligands. Metals able to coordinate strongly with unsaturated ligands are restricted to those in a small triangle around the centre of the periodic table, and designated class (b) acceptors by Ahrland et al., 0>. Class (b) acceptors include Cu(I), Rh(II), Ag(I), Pt(II) and Hg(II). However the majority of such metals form inert complexes which are either very readily oxidised or involve solubility problems. If thermodynamic stability constants are to be measured reliably, the equilibrium should be reached reasonably quickly, the reaction should be clean and the stoichiometry should be known or easily deduced. Furthermore, the equilibrium must be followed by means of suitable electrodes or changes in some physical property of the reaction mixture. The solvent is therefore important. 

Now that we have an eflScient route to metal formyl complexes, we can study the thermodynamic stability of these complexes. We have found that metal formyls are much less thermodynamically stable than the corresponding metal hydrides. Thus, metal formyl species have never been observed in the reactions of metal hydrides with CO because of the thermodynamic instability of the formyl complexes and not because of their kinetic instability. 

The greatly different thermodynamic stabilities of metal acyl and metal formyl compounds is probably attributable to the greater strength of the M-H bond (estimated 50-60 kcal mol ) compared with the M-C bond (estimated 30-40 kcal mol" ). We are now attempting to measure the heat of reaction for the conversion of a metal-formyl compound to a metal hydride. This will allow a much better estimate of the energy difference between a metal formyl complex and a metal hydride since the energy difference was too large to measure by equilibration of the species. 

The properties and reactivity of alkane and silane - - complexes are closely related to those of dihydrogen complexes. However, the thermodynamic stabilities of the complexes are much different. The silane complexes have been studied in less detail than dihydrogen complexes, but, broadly speaking, they are similar in stability to the dihydrogen complexes or only slightly less stable. Alkane complexes have been studied intensively as reactive intermediates, " but detailed structural and reactivity studies have not been conducted because alkane complexes are unstable in solution. The most detailed data have been gained by NMR spectroscopic studies of CpRe(CO)2(RH) complexes. These data imply that the metal binds in an Tj -mode to a single C-H bond of the alkane. 

Rossotti s books (29) devoted entirely to the determination of stability constants, provided a great impetus to thermodynamic studies of metal complexes. 

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